Absorption's Law - Negative proposition affects the law?

Question

This is a simple question.

It's known that the absorption's law is like the following example:

p ∧ (p V q) = p

But, if the proposition has a negation, does this affect the law? for example:

p ∧ ¬(p V q) = p

Is this correct?

Edit: Is the De Morgan's Law necessary before the Absorption's Law?

Negation like that does affect the law: your example does not hold. — Berci, Jul 13 '19 at 21:01
Hi @Berci, I've just edit the post with a new question, is that what you mean? — , Jul 13 '19 at 21:11
Use turh table to check them... In the second case, with both $p,q$ TRUE the RHS is True while the LHS is False. — Mauro ALLEGRANZA, Jul 14 '19 at 08:33

score 0 · Accepted Answer · answered Jul 14 '19 at 14:47

De Morgan's Law helps to show that no absorption law holds for your example.

(p ∧ ¬(p V q)) = (p ∧ (¬p ∧ ¬q))

By association we then can get

((p ∧ ¬p) ∧ ¬q)

But, (p ∧ ¬p) is always false, so (p ∧ ¬(p V q)) is always false also.

p can be true or false, and thus no absorption law holds for your example involving negation.

1 Answers1